CMB/kSZ and Compton-y Maps from 2500 square degrees of SPT-SZ and Planck Survey Data
L. E. Bleem, T. M. Crawford, B. Ansarinejad, B. A. Benson, S. Bocquet, J. E. Carlstrom, C. L. Chang, R. Chown, A. T. Crites, T. de Haan, M. A. Dobbs, W. B. Everett, E. M. George, R. Gualtieri, N. W. Halverson, G. P. Holder, W. L. Holzapfel, J. D. Hrubes, L. Knox, A. T. Lee, D. Luong-Van, D. P. Marrone, J. J. McMahon, S. S. Meyer, M. Millea, L. M. Mocanu, J. J. Mohr, T. Natoli, Y. Omori, S. Padin, C. Pryke, S. Raghunathan, C. L. Reichardt, J. E. Ruhl, K. K. Schaffer, E. Shirokoff, Z. Staniszewski, A. A. Stark, J. D. Vieira, R. Williamson
DDraft version February 10, 2021
Typeset using L A TEX twocolumn style in AASTeX63
CMB/kSZ and Compton- y Maps from 2500 square degrees of SPT-SZ and
Planck
Survey Data
L. E. Bleem,
1, 2
T. M. Crawford,
2, 3
B. Ansarinejad, B. A. Benson,
5, 2, 3
S. Bocquet,
6, 7
J. E. Carlstrom,
2, 3, 8, 1, 9
C. L. Chang,
1, 2, 3
R. Chown, A. T. Crites,
11, 2, 3
T. de Haan,
12, 13
M. A. Dobbs,
14, 15
W. B. Everett, E. M. George,
17, 13
R. Gualtieri, N. W. Halverson,
16, 18
G. P. Holder,
19, 20
W. L. Holzapfel, J. D. Hrubes, L. Knox, A. T. Lee,
13, 23
D. Luong-Van, D. P. Marrone, J. J. McMahon,
2, 3, 8, 9
S. S. Meyer,
2, 3, 8, 9
M. Millea, L. M. Mocanu,
2, 3
J. J. Mohr,
6, 7, 25
T. Natoli,
2, 3
Y. Omori,
2, 3, 26, 27
S. Padin,
28, 2, 3
C. Pryke, S. Raghunathan,
30, 31
C. L. Reichardt, J. E. Ruhl, K. K. Schaffer,
33, 2, 9
E. Shirokoff,
2, 3, 13
Z. Staniszewski,
34, 32
A. A. Stark, J. D. Vieira,
19, 20 and R. Williamson
34, 2, 3 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 60439 Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL, USA 60637 Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL, USA 60637 School of Physics, University of Melbourne, Parkville, VIC 3010, Australia Fermi National Accelerator Laboratory, MS209, P.O. Box 500, Batavia, IL 60510 Faculty of Physics, Ludwig-Maximilians-Universit¨at, 81679 M¨unchen, Germany Excellence Cluster ORIGINS, Boltzmannstr. 2, 85748 Garching, Germany Department of Physics, University of Chicago, Chicago, IL, USA 60637 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 60637 Department of Physics and Astronomy, McMaster University, 1280 Main St. W., Hamilton, ON L8S 4L8, Canada Department of Astronomy & Astrophysics, University of Toronto, 50 St George St, Toronto, ON, M5S 3H4, Canada High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan Department of Physics, University of California, Berkeley, CA, USA 94720 Department of Physics and McGill Space Institute, McGill University, Montreal, Quebec H3A 2T8, Canada Canadian Institute for Advanced Research, CIFAR Program in Cosmology and Gravity, Toronto, ON, M5G 1Z8, Canada Center for Astrophysics and Space Astronomy, Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder,CO, 80309 European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany Department of Physics, University of Colorado, Boulder, CO, 80309 Astronomy Department, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, IL 61801, USA Department of Physics, University of Illinois Urbana-Champaign, 1110 W. Green Street, Urbana, IL 61801, USA University of Chicago, Chicago, IL, USA 60637 Department of Physics and Astronomy, University of California, Davis, CA, USA 95616 Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA 94720 Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA Max-Planck-Institut f¨ur extraterrestrische Physik, 85748 Garching, Germany Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305 Dept. of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305 California Institute of Technology, Pasadena, CA, USA 91125 Department of Physics, University of Minnesota, Minneapolis, MN, USA 55455 Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA Physics Department, Center for Education and Research in Cosmology and Astrophysics, Case Western Reserve University,Cleveland,OH, USA 44106 Liberal Arts Department, School of the Art Institute of Chicago, Chicago, IL, USA 60603 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
Corresponding author: L. [email protected] a r X i v : . [ a s t r o - ph . C O ] F e b L. Bleem, T. Crawford, et al.
ABSTRACTWe present component-separated maps of the primary cosmic microwave background/kinematicSunyaev-Zel’dovich (SZ) amplitude and the thermal SZ Compton- y parameter, created using datafrom the South Pole Telescope (SPT) and the Planck satellite. These maps, which cover the ∼ . (cid:48)
25 forour highest-resolution Compton- y maps) and lower noise at small angular scales. In this work we detailthe construction of these maps using linear combination techniques, including our method for limitingthe correlation of our lowest-noise Compton- y map products with the cosmic infrared background. Weperform a range of validation tests on these data products to test our sky modeling and combinationalgorithms, and we find good performance in all of these tests. Recognizing the potential utility ofthese data products for a wide range of astrophysical and cosmological analyses, including studiesof the gas properties of galaxies, groups, and clusters, we make these products publicly available athttp://pole.uchicago.edu/public/data/sptsz ymap and on the NASA/LAMBDA website. Keywords:
Cosmic Microwave Background, Large-Scale Structure of the Universe, Galaxy Clusters INTRODUCTIONModern arcminute-scale resolution experiments suchas the Atacama Cosmology Telescope (ACT; Swetz et al.2011),
Planck (Planck Collaboration et al. 2011a), andthe South Pole Telescope (SPT; Carlstrom et al. 2011)have been used to make exquisite temperature and po-larization maps of the millimeter-wave sky. While thedominant signal in these observations arises from theprimary cosmic microwave background (CMB), thereis a wealth of additional information encoded in thesemaps, tracing both the interactions of CMB photonswith matter along the line of sight (e.g., CMB secondaryanisotropies, see review by Aghanim et al. 2008), as wellas the emission from objects between us and the surfaceof last scattering. The latter emission is dominated atshort wavelengths by the cosmic infrared background(CIB; e.g., Dunkley et al. 2011; Thacker et al. 2013;Viero et al. 2013; Mak et al. 2017; Reichardt et al. 2020and see Kashlinsky et al. 2018 for a recent review) andat longer wavelengths by synchrotron radiation, primar-ily from active galactic nuclei (AGN; see e.g., De Zottiet al. 2010; Everett et al. 2020; Gralla et al. 2020).In this work we focus on isolating signals from theCMB itself as well as two of the secondary CMBanisotropies: the kinematic and thermal Sunyaev-Zel’dovich (kSZ and tSZ) effects. The kSZ and tSZ ef-fects arise, respectively, from the first-order (Sunyaev &Zel’dovich 1972; Sunyaev & Zeldovich 1980) and second-order terms (Sunyaev & Zel’dovich 1970, 1972) in theequations governing the scattering of CMB photons offmoving electrons such as are found in galaxies, groups,and clusters (see e.g., Birkinshaw 1999; Carlstrom et al.2002 for a more detailed review). All three of these sig-nals offer powerful probes of cosmology, with the tSZ and kSZ additionally probing a range of astrophysicalprocesses.The CMB is, of course, one of the observational pil-lars of modern cosmology, with decades of observationshaving led to robust evidence for a spatially flat universethat arose from a hot Big Bang and whose compositionand evolution today is governed primarily by dark en-ergy and dark matter (e.g., Mather et al. 1994; Hinshawet al. 2013; Henning et al. 2018; Planck Collaborationet al. 2018; Aiola et al. 2020; Adachi et al. 2020). Ob-servations of the SZ effects complement this picture byproviding probes of the Universe at later times, par-ticularly from the epoch of reionization to the presentday. The tSZ effect, sourced primarily by the inverseCompton scattering of CMB photons off the hot gasin galaxy groups and clusters (Battaglia et al. 2012;Bhattacharya et al. 2012), enables the compilation ofmass-limited cluster samples out to the epoch of clusterformation (e.g., Bleem et al. 2015b; Planck Collabora-tion et al. 2016a; Huang et al. 2020; Bleem et al. 2020;Hilton et al. 2020). These samples, through growth ofstructure tests, have been used to provide cosmologi-cal constraints competitive with those from CMB andgalaxy surveys (Planck Collaboration et al. 2016b; Has-selfield et al. 2013; Bocquet et al. 2019). The tSZ powerspectrum, bispectrum, and related observables also arehighly sensitive to cosmology (e.g., Komatsu & Seljak2002; Bhattacharya et al. 2012; Hill & Sherwin 2013;Crawford et al. 2014; George et al. 2015; Horowitz &Seljak 2017; Coulton et al. 2018). Finally the kSZ ef-fect, while the faintest and thus far least characterized ofthese three observational probes, offers unique opportu-nities to explore the reionization history of the universe(Gruzinov & Hu 1998; Shaw et al. 2012; Park et al. 2013;Battaglia et al. 2013; Smith & Ferraro 2017; Reichardtet al. 2020) including a new pathway to constraining theoptical depth to reionization, τ (Ferraro & Smith 2018).In combination with next-generation galaxy surveys—e.g., the Dark Energy Spectroscopic Instrument (DESICollaboration et al. 2016), Euclid (Amendola et al.2018), SPHEREx (Dor´e et al. 2014), Vera Rubin Ob-servatory’s Legacy Survey of Space and Time (LSST;LSST Science Collaboration et al. 2009), and the Ro-man Space Telescope (Spergel et al. 2015)—it will alsolead to new probes of gravity and dark energy (Bhat-tacharya & Kosowsky 2008; Keisler & Schmidt 2013;Mueller et al. 2015a), massive neutrinos (Mueller et al.2015b), and other physics that influences the growth ofstructure (Bhattacharya & Kosowsky 2007; Sugiyamaet al. 2017; Soergel et al. 2018).Observations of the SZ effects also can be usedto constrain astrophysical processes. The redshift-independent nature of these signals makes them highlycomplementary to other physical probes both alone(CMB-S4 Collaboration et al. 2019), and in combina-tion with other observables (Siegel et al. 2018; Shitan-ishi et al. 2018; Okabe et al. 2020; Ruppin et al. 2020).In recent work, these signals have been used to provideinsight into the “missing baryon” problem (e.g., Tan-imura et al. 2019; de Graaff et al. 2019) by tracing thehot gas in filaments between massive galaxies, as wellas to constrain astrophysical feedback and the thermalproperties of both aggregate samples of galaxies (e.g.,Soergel et al. 2016; De Bernardis et al. 2017; Chaves-Montero et al. 2019; Schaan et al. 2020; Amodeo et al.2020; Vavagiakis et al. 2021) and in high signal-to-noisemeasurements of individual clusters (Plagge et al. 2010;Planck Collaboration et al. 2012; Romero et al. 2017;Ruppin et al. 2018).Given the power of these sky signals to probe sucha diverse and important range of scientific questions,there has been significant effort in developing techniquesto isolate these signals into single-component maps (seee.g., Remazeilles et al. 2011a,b; Hurier et al. 2013; Bobinet al. 2016; Petroff et al. 2020; Sultan Abylkairov et al.2020, amongst many works). In an idealized scenario,such maps would consist only of the desired observ-ables of interest. However, the realities of noise, wave-length coverage (particularly restricted in ground-basedobservations by available atmospheric windows), lim-ited knowledge of the spectral energy distributions ofthe various sky components (Tegmark 1998) and/or in-complete differentiability between them, and the finiteangular and spectral resolution of the available data alllimit the fidelity of the signal map reconstructions. Suchlimitations typically necessitate tradeoffs between noiseand signal purity in the reconstructed component maps. To optimize the use of available data, a number ofworks have focused on improving upon the componentmaps produced using data from Planck (e.g., PlanckCollaboration et al. 2016c,d, 2020a; Lenz et al. 2019)by combining data from ground-based experiments withthat from
Planck to leverage the higher angular resolu-tion of the terrestrial experiments and the superior noiseperformance and frequency coverage of
Planck at largeangular scales. An early example of this was Crawfordet al. (2016), in which data from
Planck was combinedwith SPT observations to produce arcminute-scale emis-sion maps of the Large and Small Magellanic Clouds fora range of emission spectra. Aghanim et al. (2019) com-bined
Planck data with 148 and 220 GHz ACT datafrom the 2008-2010 seasons (Swetz et al. 2011; D¨unneret al. 2013) to construct a 1 . (cid:48) . (cid:48) Planck and 2100 square-degrees of 98 and 150 GHzdata from the 2014-2015 ACTPol observing seasons, andMelin et al. (2020) combined data from a public SPT-SZ release (Chown et al. 2018) with that from
Planck to produce a joint
Planck +SPT cluster sample usingmatched filter techniques.In this work we describe the construction and publicrelease of a series of maps constructed through the com-bination of data from the
Planck mission with that fromthe 2500-square-degree SPT-SZ Survey (Story et al.2013). These products include component maps of thetSZ and the CMB/kSZ useful for cluster detection andfor cross-correlation analyses in which bias from fore-grounds is expected to be minimal, as well as componentmaps where various contaminating sky signals have beensignificantly reduced or removed that are more optimalfor e.g., CMB lensing reconstruction (van Engelen et al.2014; Osborne et al. 2014; Madhavacheril & Hill 2018) orother analyses in which the contaminating componentscould create significant biases in the quantities of inter-est. We also provide with this release the 95, 150, and220 GHz SPT-SZ maps used in this work. Similar to themaps used in the production of the SPT-SZ cluster sam-ple (Bleem et al. 2015b), these maps are both slightlydeeper than and have higher resolution than the mapspresented in Chown et al. (2018), which conservativelyused maps subject to the more stringent cuts from SPTpower spectrum analyses (e.g., George et al. 2015) andwere further degraded to 1 . (cid:48)
75 resolution.This work is organized as follows. In Section 2 wedescribe the data used to construct and validate the
L. Bleem, T. Crawford, et al. component map products. In Section 3 we detail theprocess by which we construct the component maps andin Section 4 we describe the resulting products. InSection 5 we describe the results of several validationtests of the maps. Finally, in Section 6 we summarizeand conclude. All public data products in this paperwill be hosted at http://pole.uchicago.edu/public/data/sptsz ymap and on the NASA/LAMBDA website. DATA AND PROCESSINGThe Compton- y parameter and CMB/kSZ maps pre-sented in this work are constructed using data from twosurveys: the 2500-square-degree SPT-SZ survey and the Planck all-sky survey, as represented in the 2015
Planck data release. The SPT and
Planck data play highlycomplementary roles in this work: data from the SPThas higher resolution and lower noise at small scales,while the
Planck data has lower noise at larger scales(multipole (cid:96) (cid:46)
Herschel Space Obser-vatory
SPIRE instrument (Pilbratt et al. 2010; Griffinet al. 2003) were used to perform systematic checks ofthe map products. In this section we summarize thesedata and their processing as relevant to the component-map construction.2.1.
The South Pole Telescope SZ survey
The South Pole Telescope (Carlstrom et al. 2011) isa 10 m telescope located approximately 1 km from thegeographic South Pole at the National Science Foun-dation Amundsen-Scott South Pole station in Antarc-tica. To date, three different generations of instru-ments have been deployed on the telescope to conductarcminute-scale observations of the millimeter-wave sky;the data used in this work were obtained between 2008to 2011 with the SPT-SZ receiver. This receiver wascomposed of six subarrays (or “wedges”) of feedhorn-coupled transition-edge bolometer sensors, with eachwedge sensitive at either 95, 150, or 220 GHz. The re-sulting SPT-SZ survey covers a ∼ h to 7 h in right ascension (R.A.)and − ◦ to − ◦ in declination (DEC); the full survey https://lambda.gsfc.nasa.gov/ In this work we make use of a number of temperatureforeground products for which the
Planck
Legacy Archivehttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php/Foreground maps footprint was subdivided and observed in 19 separatefields ranging from ∼
70 to 250 deg in size (Story et al.2013). Data was acquired by scanning the telescope backand forth across each field in azimuth and then steppingin elevation, and then repeating the scan and step proce-dure until each field had been completely covered. Onefield, centered at R.A.=21h, DEC= − ◦ , was observedin two different modes, with approximately 1/3 of thedata obtained in the azimuth-scanning mode describedabove, while the remainder was obtained in an analo-gous process by scanning the telescope in elevation andthen stepping in azimuth. One complete pass of a field,lasting roughly two hours on average, is termed an ob-servation , and each field was observed at least 200 times.Two fields, the ra5h30dec-55 and ra5h30dec-55 fields,were observed for roughly twice the total time as therest of the fields and, as a result, have roughly √ Map Making
The general procedure for converting SPT observa-tion data into field maps is presented in Schaffer et al.(2011); we briefly summarize the process here. Maps areconstructed from time-ordered bolometer data acquiredduring each scan across the field. Each detector’s datais processed to remove sensitivity to the receiver’s pulsetube cooler, cuts are applied based on both noise prop-erties and responsiveness to sources, the data is rescaledbased on the detector’s response to an internal calibra-tion source embedded in the telescope’s secondary cryo-stat, and the data is filtered and binned into map pixelswith inverse-variance weighting.Filtering of time-ordered bolometer data consists ofboth an effective high-pass filter which reduces sensi-tivity to atmospheric noise and a low-pass filter thatprevents the aliasing of high-frequency noise when thedetector data is binned into map pixels. For every scanacross the field a low-order polynomial is fit and sub-tracted from each detector’s time stream data, withthe order of the polynomial scaled to the length of thescan (roughly three modes per 10 degrees of scan forthis work). The effective (cid:96) -space cutoff of this filter isroughly (cid:96) = 50 in the scan direction. For the 220 GHzdata, which is more sensitive to large-scale atmosphericfluctuations, we also fit and subtract sines and cosinesup to a frequency equivalent to (cid:96) = 200 in the scandirection. At each time sample in the observation, anisotropic common mode filter is applied to data fromeach wedge. At 95 GHz, this common-mode filter takesthe form of subtracting the mean of all the detectors onthe wedge from the time streams, while at 150 and 220GHz, where the low-frequency atmospheric noise is moreof an issue, two spatial gradients across the wedge arealso subtracted from each detector’s data. Finally, thedata is low-pass filtered with a cutoff at angular multi-pole (cid:96) ∼ Planck data on a Fourier-mode-by-Fourier-mode basis, we donot need to mask sources in the filtering steps that pre-dominantly affect modes that can be filled in by
Planck .This includes the common-mode filtering, which acts asan isotropic high-pass filter at the detector wedge scale(roughly half a degree). We do still mask sources in thepolynomial subtraction (above a threshold of roughly6 mJy at 150 GHz), because this acts as a high-passin the scan direction only and affects modes that oscil-late slowly in the scan direction but quickly along thecross-scan direction and are thus not accessible to thelower-resolution
Planck observations. More generally,the fact that these modes are missing from both SPT-SZand
Planck data results in a small bias to the resultingCompton- y and CMB/kSZ maps, which we discuss inSection 3.4.Following the filtering, the telescope pointing modelis used to project inverse noise-variance weighted detec-tor data into map pixels. For this work the SPT singlefrequency maps are made in the Sanson-Flamsteed pro-jection (Calabretta & Greisen 2002), with a pixel scale of0.25 arcmin. Individual observation maps are coaddedwith weights determined by the average detector noiseperformance in each observation. The coadded maps areabsolutely calibrated using data from the Planck mis-sion. This calibration results in a ∼ These requirements reducethe component map areas compared to e.g., the areasearched for clusters in Bleem et al. (2015b) by slightlyshrinking the exterior boundary of the survey; the totalarea is reduced by ∼ < (cid:96) < µ K-arcmin at 95, 150, and 220 GHz respectively, Owing to asymmetry in wedge locations in the SPT-SZ focalplane (Section 2.1), the 95 and 220 GHz data have slightly re-duced coverage at opposite field edges. using the Gaussian beam approximation estimation ofSchaffer et al. (2011). For a complete listing of fielddepths, see e.g., Table 1 in Bleem et al. (2015b).2.1.2.
Noise PSDs
As in a number of previous SPT publications (e.g.,Staniszewski et al. 2009), we use a resampling techniqueto estimate two-dimensional map noise power spectraldensities (PSDs). In each resampling, individual obser-vations of a given SPT-SZ field are randomly assigneda sign of ± Angular Response Function
The SPT-SZ sky maps created as described above arebiased representations of the true sky, as the data hasbeen modified by both the finite resolution of the in-strument and the filtering processes described above.At each frequency, the instrumental response function(i.e., beam) is to first order well represented as an az-imuthally symmetric Gaussian with full width at halfmaximum (FWHM) equal to 1 . (cid:48)
6, 1 . (cid:48)
1, and 1 . (cid:48) B ( (cid:96) ).To characterize the effect of our map filtering we sim-ulate the filter response function. Following Crawfordet al. (2016), 100 simulated skies are constructed fromwhite noise convolved with a 0 . (cid:48)
75 Gaussian beam.Each sky realization is “mock observed” to obtain de-tector timestream data using the telescope pointingmodel. These time-ordered data are cut, weighted,and filtered in an identical process to the real data toform individual-observation maps. These individual-observation maps are combined with same weightingas the real data to make final coadded mock-observedmaps. For each sky realization the estimate of the filterresponse function is then determined as the ratio of thetwo-dimensional power spectrum of the coadded mapto the known input power spectrum. The 100 indepen-dent ratios are averaged and this averaged ratio is usedas the estimate of the 2D Fourier-space filter responsefunction. Because the filter transfer function is highlysimilar among all fields except the “el-scan” field (seeSection 2.1), we ran the mock observations only on the
L. Bleem, T. Crawford, et al. el-scan field and a single standard-observation field; forthe other 17 standard-observation fields we used a re-gridded version of the standard-field filter transfer func-tion. 2.1.4.
Bandpasses
The process of separating a component map signalfrom other sky signals and noise relies on a priori knowl-edge of the desired signal spectrum and, by extension,knowledge of the spectral response of the instrumentsused to collect the data. The bandpasses of the SPT-SZ detectors were characterized using a Fourier trans-form spectrometer. Spectra were measured for ∼ Planck
The European Space Agency’s
Planck satellite waslaunched in 2009 with the primary mission of conduct-ing sensitive, high-resolution observations of the CMB(Tauber et al. 2010; Planck Collaboration et al. 2011a).Full sky maps from 25-1000 GHz were produced overthe course of its multi-year mission. We make use ofproducts from the 885-day High Frequency Instrument(HFI) cold mission that are included in the
Planck
Maps, Angular Response Function, Noise Treatment
For each channel the time-ordered data is convertedinto maps as described in Planck Collaboration et al.(2014a) and updated in Planck Collaboration et al.(2016f). As detailed in the latter work, the data arecalibrated at 100-353 GHz using the time-variable CMBdipole and at 545 GHz using planetary emission fromUranus and Neptune. The absolute calibration of thefull mission HFI maps is determined to [0.09, 0.07, 0.16,0.78, 1.1(+5 model uncertainty)] % accuracy at [100,143, 217, 353, 545] GHz.The
Planck maps are processed such that the trans-fer function can be modeled as an “effective” beam—accounting for the telescope optics, survey scan strat-egy, and data processing—convolved with the map pix-elization window function (Planck Collaboration et al.2014b). We use the azimuthally symmetric “ReducedInstrument Model” (RIMO) effective beam windowfunctions derived from the 75% of the sky outside theGalactic plane. We also make use of the beam filesprovided with Planck Collaboration et al. (2020c) to ex-tend the 217 and 353 GHz beam from (cid:96) max = 4000 to (cid:96) max = 8192. Using a Gaussian approximation the typ-ical FWHM of these effective beams is [9.69, 7.30, 5.02,4.94, 4.83] arcminutes at [100, 143, 217, 353, 545] GHz(Planck Collaboration et al. 2016g). These maps areprovided in HEALPix format (G´orski et al. 2005) with N side = 2048, corresponding to 1 . (cid:48) Planck bandpasses (Planck Collabora-tion et al. 2014c).While the time-ordered
Planck data is approximately“white” with a “1 /f ” contribution at lower frequencies(Planck HFI Core Team et al. 2011), data processingand map projection can introduce correlations betweenmap pixels (Planck Collaboration et al. 2016f). In thiswork, as in Crawford et al. (2016), we ignore these non-idealities, and model the Planck noise as white noisewith levels set on a field-by-field basis. This treatmentwill not bias the resulting component maps and shouldhave only a minor effect on the optimality of the bandcombination, as the
Planck data primarily serves to fillin the large angular scale modes that have been removedor down-weighted by the SPT filtering. Noise levels areestimated using the square root of the mean of intensity-intensity variance maps in each SPT field. These noiselevels vary typically vary by 5–10% rms across the SPT-SZ fields (but up to 30% near the South Ecliptic Pole, https://wiki.cosmos.esa.int/planckpla2015/index.php/Effective Beams http://healpix.sourceforge.net where the Planck observation strategy results in verydeep coverage). The mean
Planck noise level varies byup to a factor of two between SPT-SZ fields (again par-ticularly near the Ecliptic Pole), but this is taken intoaccount as both the CMB/kSZ and Compton- y mapsare constructed independently in the 19 SPT-SZ fields.The Planck and SPT data are combined on a field-by-field basis, and then the maps constructed from in-dividual fields are stitched together to form full SPT-SZsurvey CMB/kSZ and Compton- y maps. This field-by-field procedure enables us to more optimally combine the Planck and SPT datasets given noise variations acrosseach survey. To match the SPT map projections we firstrotate the
Planck maps from the Galactic to Celestialcoordinate system using HEALPix routines. The
Planck maps are then projected using the Sanson-Flamsteedprojection to match each SPT field’s pixelization.2.3.
Treatment of Bright Sources in SPT and
Planck
Data
While data from
Planck is used to fill in missing modesat low (cid:96) removed during filtering of the SPT maps (seee.g., Sections 2.1.1, 3.4) this compensation is incompletefor time-variable signals or when a foreground sourcehas a spectral energy distribution (SED) very differentfrom the SED of the desired signal component. The for-mer effect is particularly important for bright sources(dominated by flat- or falling-spectrum blazars at theSPT wavelengths), whose flux could vary significantlybetween the time of the
Planck and SPT observations.Both of these effects can cause a mismatch in the powerin the SPT and
Planck maps, resulting in artifacts inthe output map. To mitigate such artifacts we “paintin” the regions around the brightest sources in the maps.For sources detected at >
250 mJy at 150 GHz in theSPT maps (as well as 6 additional sources from the
Planck
143 GHz source catalog (Planck Collaborationet al. 2016h) above this threshold in the
Planck but notSPT data) we fill in regions of radius 20 (cid:48) around eachsource location in all of the maps using the mean valueof the sky temperature computed from annuli extend-ing 15 (cid:48) from the inpainting radius. We do the same forsources above 150 mJy at 150/143 GHz but with a 10 (cid:48) radius. These painted regions are masked in the pro-vided source mask. 2.4.
Herschel
We tune the Compton- y reconstruction parameters tominimize the correlation with the CIB by using datafrom the Herschel Space Observatory (Pilbratt et al.2010) SPIRE instrument (Griffin et al. 2003). The
Her-schel data consists of observations at 500, 300, and 250 µ m that were acquired over a ∼
90 square-degree patchcentered at (RA,DEC)=(23h30m, − ◦ ) in the SPT-SZsurvey under an Open Time program (PI: Carlstrom).In this study we make use of the 500 µ m maps. The Herschel /SPIRE angular resolution is superior to thatof both SPT and
Planck —the effective resolution of the500 µ m maps is 36 . (cid:48)(cid:48) HI4PI
To validate the removal of Galactic dust from themaps at large scales we make use of data from the HI4PIsurvey of neutral atomic hydrogren (HI4PI Collabora-tion et al. 2016). Such HI survey data has long beenknown to be well-correlated with infrared-to-millimeter-wavelength dust emission (e.g., Boulanger & Perault1988; Boulanger et al. 1996; Lagache et al. 2003; PlanckCollaboration et al. 2014b). The survey maps in theSPT region are from the third revision of the GalacticAll Sky Survey (GASS, McClure-Griffiths et al. 2009;Kalberla et al. 2010; Kalberla & Haud 2015) whichwas conducted in 2005-2006 with the Parkes RadioTelescope. These maps have an angular resolution ofFWHM=16 . (cid:48) HI column density mapsprovided in HEALPix format. These were constructedvia integrating over the full velocity range of GASS (withabsolute radial velocity ≤
470 km s − ). Further detailson these data products can be found in HI4PI Collabo-ration et al. (2016). CONSTRUCTION OF THE CMB/KSZ ANDCOMPTON- Y COMPONENT MAPSIn this work we assume the
Planck and SPT tem-perature maps to be composed of sky signal contribu-tions from primary CMB temperature fluctuations, tSZ,kSZ, radio galaxies, the dusty galaxies that make upthe CIB, and Galactic dust; and noise contributionsfrom the instrument and—for SPT—the atmosphere.In this section we describe the procedure for extractingan unbiased component map from individual frequencymaps; the models we adopt for the instrumental, atmo-spheric, and astrophysical contributions to the variancein the individual maps and covariance between them;the treatment of the “missing modes” in output com-ponent maps; and our procedure for suppressing CIBcontamination in the “minimum-variance” Compton- y maps. 3.1. Linear Combination Algorithm
We use a linear combination of individual frequencymaps to construct the Compton- y map. The prac- L. Bleem, T. Crawford, et al. tice of linearly combining mm-wave/microwave mapsto extract individual sky components is common inthe CMB field, and there are many approaches (see,e.g., the review by Delabrouille & Cardoso 2009).All mm-wave/microwave linear-combination (LC) algo-rithms have a common goal, namely to combine a setof single-frequency maps to produce a map with unbi-ased response to a signal with a known frequency spec-trum. LC algorithms also generally seek to minimizethe variance in the output map from instrument noise,atmospheric fluctuations (if the data is from a ground-based experiment), and sources of astrophysical signalother than the target signal. For some applications, itis preferable to minimize the total variance in the out-put map, while for other applications it is preferable toexplicitly null the response of the output map to oneor more signals (assuming the SEDs of those signals areknown perfectly). An example of the latter type of mapis a map of the CMB temperature fluctuations that hasnull response to tSZ, which can be a significant contam-inant to measurements of CMB lensing and the kSZ ef-fect (e.g., Madhavacheril & Hill 2018; Baxter et al. 2019;Raghunathan et al. 2019).Another choice that must be made in constructing theLC is how to characterize the variance in the individualfrequency maps and the covariance between them. Onechoice is to use models of the various sources of powerin the maps, including instrumental and atmosphericnoise as well as astrophysical signals. The downside ofthis approach is that if the models are not perfect, therewill be excess residual variance in the output compo-nent map(s). Another approach, referred to as “inter-nal linear combination” or “ILC” in the literature, esti-mates the variance and covariance from the individualfrequency maps themselves. The downside to this ap-proach is that it results in a biased output map (e.g., De-labrouille et al. 2009). This “ILC bias” can be mitigatedby averaging the covariance estimates over many real-space or Fourier-space pixels. The ILC approach withFourier-space averaging was used to produce the ACT-Pol+
Planck
Compton- y map in Madhavacheril et al.(2020). We choose to adopt the first approach, prefer-ring to incur a potential noise penalty than a bias in theoutput map. We estimate the potential excess variancefrom imperfect modeling in Section 5.1.Operationally, this approach is identical to the mapcombination procedure used in the construction of theSPT-SZ cluster sample (e.g., Melin et al. 2006; Bleemet al. 2015b), replacing the β -profile filter used to op-timize cluster identification with a profile with a flatresponse as a function of (cid:96) . In this approach, eachsingle-frequency map at sky location n is characterized as a sum over the various sky signal components, con-volved with the appropriate beam and transfer function(see Section 2.1.3), plus instrumental—and in the caseof SPT, atmospheric—noise. T ( ν i , n ) = R ( ν i , n ) ∗ (cid:88) j f j ( ν i ) S j ( n ) + n noise ( ν i , n ) , (1)where R ( ν i , n ) = B ( ν i , n ) ∗ F ( ν i , n ) is the convolutionof the real-space beam and filter kernel, and f j ( ν ) is theSED of signal S j . We choose to work in two-dimensionalFourier space, using l as the wavenumber-like Fourierconjugate of sky location n , in which case we can writeEquation 1 as T ( ν i , l ) = R ( ν i , l ) (cid:88) j f j ( ν i ) S j ( l ) + n noise ( ν i , l ) , (2)where the R ( ν i , l ) = B ( ν i , (cid:96) ≡ | l | ) F ( ν i , l ) is the productof the Fourier-space beam window function (which weapproximate as azimuthally symmetric) and filter trans-fer function (which is manifestly anisotropic for SPT-SZ).As shown in Melin et al. (2006) and (in an alternatederivation) in Appendix B, under the assumption thatthe instrumental/atmospheric and astrophysical noisemodels are correct, the combination of the data thatyields the minimum-variance, unbiased map of signal S with SED f ( ν ) in two-dimensional Fourier space is:¯ S ( l ) = (cid:88) i ψ ( ν i , l ) T ( ν i , l ) , (3)where ψ ( ν i , l ) = σ ψ ( l ) (cid:88) j N − ij ( l ) f ( ν j ) R ( ν j , l ) , (4)is the weight contributed to the output map ¯ S by band ν i at angular frequency l , σ ψ ( l ) is the predicted varianceof the output map at angular frequency l , given by σ − ψ ( l ) = (cid:88) i,j f ( ν i ) R ( ν i , l ) N − ij ( l ) f ( ν j ) R ( ν j , l ) , (5)and N ij ( l ) is the two-dimensional Fourier space versionof the band-band, pixel-pixel covariance matrix, includ-ing contributions from instrumental and atmosphericnoise, and from sky signals other than the signal of in-terest. The model used to construct N is presented inSection 3.2. We normalize N so that the squared, az-imuthally averaged Fourier-domain power as a functionof (cid:96) = | l | is equivalent to C ( (cid:96) ) in the flat-sky limit.To make a map of signal S with some other signalformally nulled, we simply replace f in the previousequations with an N bands × N components matrix f i ( ν j ) en-coding the spectral behavior of all signals for which wedesire independent output maps. The band-weightingfunction ψ then becomes an N bands × N components ma-trix at each two-dimensional Fourier location, and theoutput component maps ¯ S i are given by¯ S i ( l ) = (cid:88) j ψ i ( ν j , l ) T ( ν j , l ) , (6)where ψ i ( ν j , l ) = (cid:88) k,m C ψ,ik ( l ) N − km ( l ) f j ( ν m ) R ( l , ν m ) , (7)and C − ψ,ij ( l ) = (cid:88) k,m f i ( ν k ) R ( ν k , l ) N − km ( l ) f j ( ν m ) R ( l , ν m ) . (8)We show in Appendix C that for the particular case oftwo components this band-weighting function is iden-tical to Equation 3 in Madhavacheril et al. (2020), asderived in, e.g., Remazeilles et al. (2011a).There is an important assumption implicit in this for-mulation, namely that the statistical behavior of theinstrumental/atmospheric noise and the astrophysicalcontaminants does not vary across the maps. This al-lows the noise and contaminants to be meaningfully rep-resented in Fourier space and (under the assumptionof Gaussianity) means that the Fourier components atdifferent frequencies are independent, so that ψ can becomputed independently at every value of l . This is agood approximation for the noise in the SPT-SZ survey,particularly because we perform the component separa-tion in each of the 19 SPT-SZ fields individually. TheSPT-SZ noise in these fields only varies slightly as afunction of declination, and the Planck noise across anyone of these ∼
200 deg regions is fairly uniform as well(see Section 2.2.1). Most of the relevant astrophysicalcomponents are both statistically isotropic across theSPT-SZ fields and Gaussian-distributed, with the no-table exceptions of Galactic dust and synchrotron andindividual bright emissive sources and galaxy clusters.The SPT-SZ fields are at high Galactic latitude, andat the angular scales relevant for tSZ studies Galacticforegrounds are negligible in these fields—though at thevery largest angular scales, Galactic dust is clearly vis-ible in the resulting Compton- y map if we do not cor-rect for it, see Section 3.3 for details. Meanwhile, wemask all emissive sources down to flux densities of ∼ Sky and Noise Model
In this section, we describe the model used to con-struct the spectral behavior matrix f i ( ν j ) and the two-dimensional Fourier-space covariance matrix N ij ( l ) usedin the LC algorithm described in Section 3.1. N ij ( l ) in-cludes contributions from astrophysical sources and in-strumental and atmospheric noise, and it includes co-variance between maps at different observing frequen-cies. We model the amplitude and angular power spec-tra of the astrophysical contributions to the SPT-SZand Planck maps based on recent power spectrum re-sults from the SPT and
Planck collaborations, while thenoise model is based on the estimates described in Sec-tions 2.1.2 and 2.2.1.The contributions to the sky signal are modeled asfollows: • The tSZ appears as a spectral distortion of theCMB spectrum in the direction of energetic elec-trons, such as those found in galaxy groups andclusters. In this work we follow Sunyaev &Zel’dovich (1972); Sunyaev & Zel’dovich (1980)where this distortion at a given frequency, ν , isgiven by:∆ T ( ν ) = T CMB f SZ ( x ) (cid:90) n e k B T e m e c σ T dl ≡ T CMB f SZ ( x ) y SZ , (9)where the integral is along the line of sight, T CMB =2 . ± . x ≡ hν / k B T CMB , k B is the Boltz-mann constant, c the speed of light, n e the elec-tron density, T e the electron temperature, σ T theThomson cross-section, and f SZ ( x ) is the frequencydependence of the effect relative to the spectrum offluctuations of a 2.73K blackbody (note that we as-sume that all input maps are calibrated such thatthey have unit response to CMB fluctuations): f SZ ( x ) = (cid:18) x e x + 1 e x − − (cid:19) (1 + δ rc ) , (10)with δ rc encompassing relativistic corrections (e.g.,Wright 1979; Nozawa et al. 2000; Chluba et al.2012). While these relativistic corrections canhave a significant impact on the tSZ signal at e.g.,the locations of hot clusters (e.g., Hurier 2016), inthis work, at small angular scales where this newCompton- y map will offer significant advantages0 L. Bleem, T. Crawford, et al. over the
Planck data previously available in thisregion, omitting these corrections has negligibleimpact on the weights in the band combination.At high (cid:96) (see Figure 1) the y map constructionis dominated by a combination of the SPT 95 and150 GHz channels and the difference in the relativestrength of the tSZ signal in these bands when in-cluding relativistic corrections is small (for exam-ple the ratio of f SZ in the 95/150 GHz bands for a15 keV cluster is 1.70 when including relativisticcorrections compared to 1.71 without). The am-plitude at the location of hot gas will be biasedlow however, e.g., 8% (3.5%) for 15 (5) keV gas(Nozawa et al. 2000). • The primary CMB is modeled following the powerspectrum results presented in Planck Collabo-ration et al. (2020d). In particular we usethe temperature power spectrum predicted bythe best-fit cosmological model to the
Planck plikHM TTTEEE lowl lowE lensing dataset. • The CIB is modeled based on the results of Re-ichardt et al. (2020) from the SPT-SZ and SPTpolsurveys. It is parameterized into two components:a Poisson component whose power spectrum is in-dependent of angular scale and a clustered compo-nent that follows the one and two halo clusteringtemplate of Viero et al. (2013). Both componentsare assumed to have a scaling with frequency thatfollows a modified black body: η ν = ν β B ν ( T ) (11)where B ν is the black-body spectrum for a tem-perature T and β is the dust emissivity index. Fora fixed dust temperature of 25 K, Reichardt et al.(2020) constrains β P = 1 . ± .
13 for the Pois-son component and β cl = 2 . ± .
18 for the clus-tered term with 150 GHz power at (cid:96) = 3000 of D P3000 = 7 . ± . µ K for the Poisson com-ponent and D one − halo3000 = 2 . ± . µ K and D two − halo3000 = 1 . ± . µ K for the one- and two-halo terms, respectively. • We adopt a two-fold approach to reduce contam-ination from Galactic cirrus. As described belowin Section 3.3, at large angular scales we subtractoff a template of the dust emission from each of Where D refers to power at (cid:96) = 3000 in the convention D (cid:96) = (cid:96) ( (cid:96) +1)2 π C (cid:96) . the single-frequency maps used in the analysis. Atsmaller angular scales we incorporate the dust sig-nal as a component in our noise covariance matrix.We assume that this cirrus signal is well repre-sented by a modified blackbody that is 100% cor-related between bands with a dust temperatureof 19 K (Viero et al. 2019), a dust emissivity of β cirrus = 1 .
89 (Martin et al. 2010), and a spatialdependence of D (cid:96) ∝ (cid:96) − . which we further reduceat large angular scales to correct for the powerremoved by the template subtraction. The ampli-tudes of the cirrus signal at each frequency is setby scaling the results of George et al. (2015). • We include a Poisson component for the radiosource power based on the results of Reichardtet al. (2020) which found a spectral index, ν α , α = − .
76 and amplitude D = 1 . ± . µ K for sources fainter than 6.4 mJy at 150 GHz inSPT data. We also provide a mask with the loca-tion of sources detected above this threshold (Ev-erett et al. 2020). After applying this mask wediscuss residual contamination from sources belowthis threshold in Section 5.1.As discussed in the previous section, the intrinsic two-dimensional fluctuation power from all of these signalsis expected to be statistically isotropic except for Galac-tic foregrounds and individual bright emissive sources,which we argue contribute negligibly to the covariancematrix. Sky signals that contribute significantly to thecovariance are also expected to be isotropic on the sky(no preferred direction). In this case, we can write (cid:104) S j ( ν i , l ) S j ( ν k , l ) (cid:105) = C ( ν i , ν j , (cid:96) = | l | ) δ ( l = l )(12)and characterize the signal power with an independentband-band covariance matrix only dependent on (cid:96) ≡ | l | .As discussed in Sections 2.1.2 and 2.2.1, we can alsoapproximate the SPT-SZ and Planck noise as statisti-cally isotropic (and thus uncorrelated between different l modes). Because of the combination of the SPT scanpattern and low-frequency noise from atmosphere andother sources, the noise part of the covariance matrixis not isotropic on the sky (modes that oscillate quicklyalong the SPT scan direction are less noisy than thosethat oscillate slowly along that direction). For this rea-son we keep the full two-dimensional noise covariance N noise ij ( l ). 3.3. Galactic Dust
While the SPT-SZ fields were generally chosen to tar-get areas of high Galactic latitude, there is still apprecia-ble emission at large angular scales from Galactic dust.1 W e i gh t s [ a r b . ] tSZ Weight, Minimum-variance SPT, 95 GHzSPT, 150 GHzSPT, 220 GHzPlanck, 100 GHzPlanck, 143 GHzPlanck, 217 GHzPlanck, 353 GHz W e i gh t s [ a r b . ] tSZ Weight, CMB-nulled W e i gh t s [ a r b . ] CMB/kSZ Weight, tSZ-nulled
Figure 1.
Relative azimuthally averaged band weights for the minimum-variance thermal SZ Compton- y map ( upper left ),the CMB-nulled y map ( lower left ), and the tSZ-nulled CMB/kSZ map ( lower right ). As this emission is spatially variable across the surveyfootprint we choose to subtract a template of this con-taminant from each frequency map before including it inour Fourier-based map construction. We explored con-structing this template using data from the HI4PI sur-vey (HI4PI Collaboration et al. 2016), the
Planck ther-mal dust map constructed using the generalized needletinternal linear combination (GNILC) technique (PlanckCollaboration et al. 2016i), and the CMB-subtracted
Planck
545 GHz “foreground” map constructed usingthe COMMANDER algorithm (Planck Collaborationet al. 2016c). Ultimately we settled on using the 545GHz foreground map smoothed to a FWHM of 16 (cid:48) toconstruct our template, validating the dust removal us-ing the HI4PI survey. We note that while the GNILCthermal dust map has superior dust modeling, its reso-lution is spatially varying (with FWHM ranging from 5 (cid:48) to 21 . (cid:48) Planck frequency map we first project both the 545 GHz foreground template map and the COMMAN-DER foreground map for the
Planck frequency of inter-est onto each of the SPT fields. We smooth each map toa resolution of 16 (cid:48) as we are interested in determining thescaling between Galactic dust and the
Planck frequencymaps and do not want to include the smaller-scale CIBin our fits and subtraction here. We next rebin the datato 4 (cid:48) pixels and mask bright emissive sources detected at > σ in SPT data at 95 or 150 GHz with degree-radiusmasks to reduce spurious correlations between the maps.We conduct an outlier-resistant polynomial fit over allthe SPT-SZ fields to find the global relation (one perfrequency for the whole survey) between the intensityin the template and the various smoothed foregroundmaps, finding a cubic polynomial to provide the bestfit. The smoothed 545 GHz foreground maps are thenscaled by this relation and subtracted off from each ofthe Planck full sky maps before they are used in the LCdescribed above.We also fit for a similar correlation using the SPTdata, this time additionally filtering the 545 GHz tem-plate map with the SPT transfer function. However, thehigh-pass filter applied to the SPT maps has already ef-fectively removed the majority of the large scale emis-2
L. Bleem, T. Crawford, et al. sion and no significant correlation was detected, evenreducing the smoothing of the maps to a FWHM of 10 (cid:48) .Given the small SPT data contribution at the (cid:96) rangesaffected (see e.g., Figure 1), we choose to simply ignorethe low- (cid:96) dust contribution to the SPT maps (but doinclude a dust covariance matrix as a source of noise inthe map combination, as detailed above).The nature of the Galactic emission is not uniformacross the full SPT-SZ survey. In particular, in areasof high dust intensity—such as are found at the westernedges of the SPT-SZ fields closest to the Galaxy—thissimple cubic polynomial correction breaks down. Thisis expected, as previous works have shown that regionswith bright cirrus also have significant contribution fromdust emission associated with molecular gas which fol-lows a different modified black body function than re-gions correlated with HI (see discussion in e.g., PlanckCollaboration et al. 2011b). Given the relative weightsof the frequency channels in the map construction, suchincomplete subtraction of dust emission results in a re-duction in the recovered tSZ signal at large-scales in verydusty regions. While this bias will not affect analysesconducted on smaller-scale features (e.g., cluster detec-tion at z > .
25, tSZ profiles on scales smaller than theemission, etc.) we do include pixel masks encompassingregions of poorer dust subtraction for those who wish toexclude these regions from their analysis. These masksare constructed from the smoothed 545 GHz foregroundmaps in regions with emission > . > σ away from zero. As a checkof our dust removal, we cross-correlate our minimum-variance and CIB/CMB-nulled Compton- y maps withthe HI map provided with the HI4PI survey finding thecross-correlation power reduced by 7-10 × , respectivelyfollowing this dust removal procedure. In Figure 2 weshow one SPT field, ra5h30dec-55 , before and after re-moving Galactic dust.3.4. Treatment of Missing Modes
As mentioned in Section 2.1.1, the SPT scanningstrategy and data filtering results in a set of two-dimensional Fourier modes on the sky being removedfrom the SPT-SZ maps used here. In particular,the polynomial filtering of the SPT-SZ detector time-ordered data removes modes at low frequency alongthe scan direction. For nearly all observations, SPT isscanned along lines of constant elevation, which, at thegeographic South Pole, correspond to lines of constantdeclination. In the Sanson-Flamsteed projection used inthis work, lines of constant declination are parallel to the x -axis; thus, the SPT-SZ maps used here have no infor- Figure 2.
Left panel:
Minimum-variance Compton- y mapfor the SPT-SZ ra5h30dec-55 field constructed without cor-recting for large scale dust emission. Right panel:
The samefield after correcting for this emission as discussed in Section3.3. The maps are smoothed with a beam of FWHM = 5 (cid:48) for display purposes. mation at the lowest values of l x , or angular frequencyalong the horizontal map direction. Planck data is notmissing these modes, so the LC algorithm uses
Planck data exclusively in this region of Fourier space. At high (cid:96) = | l | , the Planck data is heavily rolled off by the fi-nite angular resolution of the instrument, and the factorneeded to restore these modes to an unbiased estimateof CMB/kSZ or Compton- y multiplies the Planck noise,resulting in the high- l y , low- l x part of Fourier space be-ing many times noisier than average.We have chosen to suppress this noise by applying atwo-dimensional Fourier-space filter to the output com-ponent maps. This filter is equal to unity everywhere ex-cept in the “trough” of modes at low l x —in this troughthe filter is equal to a Gaussian in l y , with σ l y set suchthat the noise is roughly equal to the noise outside thetrough. We include two-dimensional ( l x , l y ) and one-dimensional ( (cid:96) -space) versions of this filter as one of thedata products in our release; these can be used as an ef-fective transfer function or (cid:96) -space beam in power spec-trum or correlation analyses. For object-based analysessuch as aperture photometry, we estimate the bias fromthis filter in Section 4.1.3.5. CIB Contamination vs. Noise in“Minimum-variance” y Map
As discussed above, the band weighting in the single-component version of the linear combiner (in which noother signals are explicitly nulled) produces the mini-mum total variance in the resulting Compton- y map.But some sources of variance are of more concern thanothers, and for a y map, the presence of CIB in the mapis generally of the highest concern, particularly for us-ing that y map in cross-correlation studies. One canattempt to null a component of the CIB with a par-3 y i × C I B / y × C I B CIB x 1CIB x 3CIB x 5CIB x 7CIB x 8CIB x 9 0 2 4 6 8 10 12
CIB multiplier c r o ss - s p ec t r u m r a ti o a t = o r =1000 ratio, normal field=1000 ratio, deep field=4000 ratio, normal field=4000 ratio, deep field R M S ( y i ) / R M S ( y ) noise ratio, normal fieldnoise ratio, deep field Figure 3.
Left panel: y -CIB cross-spectrum for different CIB covariance multiplier values (see text for details) relative tothe y -CIB cross-spectrum for a y map made just from dividing a 150 GHz map by the tSZ factor for that frequency. Solidlines show results using band weights created assuming normal-depth SPT-SZ field noise; dashed lines show results using bandweights created assuming “double-depth” SPT-SZ field noise. Right panel: y -CIB cross-spectrum ratio (as defined in the ploton the left) at (cid:96) = 1000 and (cid:96) = 4000 and total y -map rms as a function of CIB multiplier. Normal-depth and double-depthresults are shown in dark- and light-shaded lines, respectively. From this plot it is clear that a significant reduction in y -CIBcorrelation can be achieved with a small noise penalty. ticular SED, as we do in the three-component versionof the map we create, but that results in a fairly highnoise penalty and does not fully solve the problem, asthe CIB is a combination of many components with dif-ferent SEDs. Multiple components with different SEDscan be nulled, but this is limited by the number of fre-quency bands (and further increases the noise penalty).Here we investigate trading off CIB for noise andCMB variance by artificially increasing the weight ofthe CIB in the linear combiner—effectively lying to thealgorithm about how bright the CIB is. We find thatmultiplying the CIB part of the covariance by someamount is quite effective in reducing the CIB compo-nent in the resulting y map while only causing mild in-creases in total variance. We measure the level of CIBin the synthesized “minimum-variance” y map by cross-correlating the Herschel /SPIRE 500 µ m map describedin Section 2.4 with the y map from the SPT-SZ fieldthat overlaps with the Herschel /SPIRE coverage.Figure 3 shows that cross-correlation as a function ofCIB covariance multiplier. Specifically, the left panel ofFigure 3 shows the ratio of the CIB- y cross-spectrumto the cross spectrum of the CIB with a y map madejust by dividing an SPT-SZ- Planck synthesized 150 GHzmap by f SZ (150 GHz) T CMB , with different curves repre-senting different values of the CIB multiplier. The right We note that this is effectively a less mathematically rigorousversion of the Partially Constrained ILC method proposed inSultan Abylkairov et al. (2020). panel shows that ratio at two specific (cid:96) values ( (cid:96) = 1000and (cid:96) = 4000) as a function of CIB multiplier, along withthe total map rms relative to the true minimum-variance y map (in which the “CIB multiplier” is unity). In bothplots, different curves are shown for band weights syn-thesized assuming the noise in the normal SPT-SZ fielddepths and for band weights synthesized assuming thenoise in the “double-deep” fields. It is clear that theCIB- y cross spectrum can be reduced significantly (ef-fectively to zero at (cid:96) = 4000) with only a mild ( (cid:46) y map, wechoose a CIB multiplier value of eight for the normal-depth fields and five for the double-depth fields. Whenwe use the term “minimum-variance map” anytime inthe rest of this work, we are actually referring to thesemaps. Finally we note that we do not apply this CIBmultiplier to the covariance when we produce y or CMBmaps with a component of the CIB formally nulled. THE CMB/KSZ AND COMPTON- Y MAPSWe make and release several versions of componentmaps resulting from our LC algorithm: • a “minimum-variance” y map. This product isconstructed using band weights defined in Equa-tions 3–5. Assuming the signal and noise modelsare correct, and with no modifications to the in-put covariance, this product formally has the low-est variance possible for an unbiased estimate of y on all scales. However, as discussed above, we domodify the covariance to reduce the correlation of4 L. Bleem, T. Crawford, et al. h h h h h h h h -20°-30° D ec li n a ti on ( J ) CMB/kSZ K C M B -20°-30° Right Ascension (J2000) D ec li n a ti on ( J ) Compton-y y × Figure 4.
Two examples of component maps provided in association with this work. (Top) tSZ-nulled CMB/kSZ mapconstructed using observations from the 2500d SPT-SZ survey and
Planck
HFI. (Bottom)
Minimum-variance Compton- y mapfrom the same. Both of these maps are smoothed here for display purposes; we provide minimum-variance map products at1 . (cid:48)
25 resolution and map products with other signals nulled at 1 . (cid:48)
75 resolution in the data release. this map with the CIB (as traced by 500 µ m Her-schel /SPIRE data), at the cost of a small (order10%) penalty in total y -map rms. We neverthelesswill refer to this map as the “minimum-variance’map” (or “single-component map”) in the remain-der of this work. • a “CMB-nulled” y map and the corresponding y -nulled CMB/kSZ map. We also refer to these asthe “two-component” maps. • a “CMB- and CIB-nulled” y map and the corre-sponding y - and-CIB-nulled CMB/kSZ map and y - and CMB-nulled CIB map. We also refer to these as the “three-component” maps. Becausethe CIB is made up of many independent emittersat different redshifts and temperatures (and differ-ent compositions), it is not possible to null all theCIB emission with a single SED. For our three-component maps, we choose to null CIB emis-sion with an SED equal to the best-fit Poisson-component SED in George et al. (2015), who findthat this component is the largest contribution tothe (cid:96) = 3000 power at 150 GHz. As expected, thenoise levels of the two- and three-component prod-ucts are significantly higher than for the minimum-variance case.5As an example of two of the data products we pro-vide, we show the full-survey versions of the tSZ-nulledCMB/kSZ and the minimum-variance Compton- y mapsin Figure 4. We provide flat-sky full and half (sur-vey+mission) maps in each of the 19 SPT fields at 0 . (cid:48) N side = 8192. The minimum-variance single-componentdata products are provided at 1 . (cid:48)
25 resolution and themulti-component products at 1 . (cid:48)
75 resolution.Figure 1 shows the relative band weights ( ψ fromEquation 4 or ψ i from Equation 7) as a function of (cid:96) = | l | for three of the maps discussed above. As expected,the Planck bands provide the bulk of the informationat low (cid:96) (large angular scales), where the SPT-SZ datais contaminated by atmospheric fluctuations. At higher (cid:96) (smaller angular scales), the higher angular resolutionand lower instrument noise levels of the SPT-SZ datatake over. Also notable is the similarity of the single-component and two-component tSZ weights at low (cid:96) , un-derstandable as the primary CMB is the largest sourceof variance at these scales. The tSZ-nulled CMB/kSZweights are dominated at low (cid:96) by the
Planck
217 GHzdata, which is close to the tSZ null, but at high (cid:96) allthree SPT-SZ bands contribute, in part because of thehigher relative noise in the SPT-SZ 220 GHz data.4.1.
Bias to Aperture Photometry From Missing Modes
As discussed in Section 3.4, the maps produced inthis work have two filters applied after the beam-and-transfer-function-deconvolved individual frequencymaps have been combined into synthesized componentmaps. One filter is a simple Gaussian smoothing withfull width at half maximum of 1 . (cid:48)
25 for the single-component y map and 1 . (cid:48)
75 for the multi-componentmaps. The non-standard filter is an anisotropic low-pass filter that only affects modes that oscillate slowlyin the direction of right ascension. The motivation forthis filter is discussed in Section 3.4; here we calculatethe bias incurred to aperture photometry if this filter isignored.We estimate this bias by creating simulated galaxycluster profiles, Fourier transforming, multiplying bythis l -space filter, inverse-Fourier transforming, and per-forming aperture photometry on these simulated pro-files. We compare the results of aperture photometryon the filtered profiles to results of aperture photome-try on the original cluster profiles and report the dif-ference as the bias from the filter. We perform thiscalculation on a range of cluster masses and redshiftsand using a range of aperture radii. We use the Arnaudet al. (2010) model for the cluster y profile. For cluster Figure 5.
Top panel:
Azimuthally averaged Compton- y profiles for ACO 3667 at z = 0 . Bottom panels : On theleft is a cutout from the
Planck
Compton- y map (Planck Col-laboration et al. 2016d) centered on the cluster. We makea similar cutout on the right from the minimum-varianceCompton- y map presented in this work. The arcminute-scalecircular decrements in this image are located at the locationsof bright radio sources readily detected in SPT data, enablingus to mask these regions when measuring the cluster’s pres-sure profile. masses 0 . × M (cid:12) < M < × M (cid:12) , redshifts0 . < z <
2, and aperture radii 1 . (cid:48) < r < . (cid:48) , we finda maximum bias of ∼ r > (cid:48) the maximum bias is ∼ Comparison to Other Releases
To date, the only other publicly available Compton- y maps in the SPT-SZ survey footprint are derived from Planck data products (particularly Planck Collabora-tion et al. 2016d). As expected, the addition of SPTdata products significantly improves both the angularresolution (from 10 (cid:48) to 1 . (cid:48)
25 or 1 . (cid:48)
75, for the minimumvariance and component-nulled versions, respectively) aswell as the noise performance at small scales. We pro-vide a qualitative demonstration of this effect in Figure5 where we highlight the ability of the new data prod-ucts to constrain arcminute-scale features in the pressureprofile of Abell 3667 (Duus & Newell 1977; Abell et al.1989) at redshift z = 0 . L. Bleem, T. Crawford, et al. for which the improved angular resolution allows us toresolve features on ∼
80 kpc scales. This significant im-provement in resolution will also aid in the detection ofhigher-redshift clusters; we detail the results of a blindcluster search below in Section 5.2.As mentioned in the introduction, arcminute-scalecomponent maps—including minimum-variance andCMB-nulled Compton- y maps and a y -nulled CMB/kSZmap—constructed from Planck and ACT data were pre-sented in Madhavacheril et al. (2020). In Figure 9 of thatwork, the authors showed that the power spectra of the y and CMB/kSZ maps including ACT data were (asexpected) signal-dominated to much higher multipolevalues (smaller scales) than corresponding maps from Planck alone. In turn, we compare the power spectraof the maps in this release to those from the two skyregions in Madhavacheril et al. (2020)—the ∼ BOSS North or BN field and a deeper ∼ fieldreferred to as D56—in Figure 6.There are many features worth noting in Figure 6.First, the agreement in the signal-dominated multipoleregions—in particular of the CMB/kSZ map (bottomleft panel)—demonstrates that the output maps fromthe two works are statistically consistent at the 10% levelor better. This is not surprising, especially because themaps from both works are dominated by Planck data atthese angular scales, but it is a rough validation of bothpipelines.The amplitudes of the power spectra in the noise-dominated multipoles merit further discussion. Asshown in Figure 1 in this work and Figure 5 inMadhavacheril et al. (2020), the high- (cid:96) ( (cid:96) (cid:38) y map weights are dominated bythe 150 GHz SPT / 148 GHz ACT data. The typi-cal SPT-SZ noise level at 150 GHz ( ∼ µ K-arcmin)is between the 148 GHz noise levels in the two ACTregions ( ∼
25 and ∼ µ K-arcmin in BN and D56, re-spectively, cf. Table 1 in Madhavacheril et al. 2020), soit is not surprising that the high- (cid:96) power spectrum ofthe SPT-SZ “minimum-variance” y map lies in betweenthat of the two ACT regions. By contrast, the SPT-SZhigh- (cid:96) power spectrum is below that of both ACT re-gions for both components of the two-component linearcombination (the CMB-nulled y map and the y -nulledCMB/kSZ map). This is especially surprising given thatthe 98 GHz ACT noise levels in the D56 region ( ∼ µ K-arcmin) are significantly lower than the SPT-SZ 95 GHznoise.The two features of the data used in the SPT-SZlinear combination that could account for this are: 1)data from the SPT-SZ 220 GHz band are included; 2)the SPT-SZ data are at slightly higher resolution, ow- ing to the 10-meter SPT primary mirror compared tothe 6-meter ACT primary (though the diameter of theprimary region illuminated by the SPT-SZ camera iscloser to eight meters). In the bottom-right panel ofFigure 6, we show that both of these features contributeto the lower SPT-SZ noise in the two-component maps.The dot-dashed line shows the predicted ACT-D56 y -nulled CMB/kSZ power spectrum if 220 GHz data (withroughly the SPT-SZ noise level) are added, and the dot-ted line shows that power spectrum if 220 GHz data areadded and if the resolution in all bands is improved bya factor of 1.33 (the ratio of the diffraction limits of 6-meter and 8-meter apertures). This result demonstratesthe utility of higher-frequency data and higher angu-lar resolution in component separation, particularly forthe goal of extracting the tSZ-nulled kSZ signal out to (cid:96) ∼ . VALIDATION OF THE COMPONENT MAPSIn this section we detail several characterization anal-yses of the SPT-SZ +
Planck component maps describedin the previous section. As discussed in Section 4.2, arough validation of the maps, particularly the y -nulledCMB/kSZ map is provided by comparing the powerspectrum of maps from this analysis to the power spec-trum of ACT+ Planck maps in Figure 6; we apply morequantitative measures in this section. These tests in-clude validation of our assumptions for the input signalmodel, tests of the blind detection from SZ clusters inthe maps, and finally, a cross check of our tSZ nullingin the CMB/kSZ map products.5.1.
Validation of the Input Signal Model
As discussed in Section 3, the linear combination al-gorithm we use relies on models of the power in vari-ous sky components, including the cross-power betweendifferent frequencies. Even if these models are wrong,the resulting CMB/kSZ or Compton- y map (or othercomponent maps) will still have unbiased response tothe desired signal (provided the instrument bandpassesare correctly measured), but the linear combination ofbands used may not be optimal; i.e., there can be ex-cess variance induced by the incorrect modeling of skysignal.Figure 7 shows a simple check of the signal model-ing, namely the power spectrum of the output y map inthe case where the CMB/kSZ and one component of theCIB are explicitly nulled. The data points are an aver-age over power spectra from the 19 individual SPT-SZfields, calculated using the cross-spectrum of one half ofthe data against the other to eliminate noise bias. Thedata points are corrected by the 1 . (cid:48)
75 smoothing beam7 yy × Minimum-variance y map
This WorkACT D56ACT BN 1000 2000 3000 4000 5000 600010 yy × y map, CMB-nulled This WorkACT D56ACT BN1000 2000 3000 4000 5000 600010 TT [ K ] CMB map, y-nulled
This WorkACT D56ACT BN 1000 2000 3000 4000 5000 600010 TT [ K ] CMB map, y-nulled, predicted
This WorkACT D56ACT D56, add 220 GHzACT D56, add 220 GHz, 8m primary
Figure 6.
Angular power spectra of selected output maps, with results from ACT+
Planck (Madhavacheril et al. 2020) shownfor comparison. The agreement between the three curves in the signal-dominated multipole region ( (cid:96) (cid:46) (cid:96) (cid:46)
Top left : Power spectra of the minimum-variance y maps from this work and fromthe two different sky regions used in Madhavacheril et al. (2020). Top right : Similar for the CMB-nulled y map. Bottom left :Similar for the y -nulled CMB/kSZ map. Bottom right : Predicted power spectra for the y -nulled CMB/kSZ map from SPT andthe ACT D56 region, using noise levels reported in this work and Table 1 of Madhavacheril et al. (2020). To demonstrate theimportance of high-frequency data and angular resolution in the component-separation process, curves for ACT D56 noise levelsare shown in the hypothetical scenario in which 220 GHz data (at the rough noise levels of the SPT data) are added and inwhich the resolution of the ACT data is improved (see text for details). and the “trough filter” (see Section 3.4) applied to themaps, but no other corrections are made (e.g., for modecoupling). Error bars are calculated using resampling(with replacement) of the values from the individualfields. Overplotted are the expected power from vari-ous sky signals given the input model and the real bandweights ψ i ( ν j ) returned by the linear combiner. Themodel for the tSZ is the best-fit model from Reichardtet al. (2020). The subtraction of the dust template de-scribed in Section 3.3, constructed by smoothing the Planck
COMMANDER 545 GHz foreground map to 16 (cid:48) resolution, will affect the low- (cid:96)
CIB power in the out-put y map; for the purposes of this plot we bracket the possible effect by multiplying the residual CIB power inthe model by a 16 (cid:48) -FWHM Gaussian, subtracting thatfrom the model, and plotting the result as a second setof model lines. The shaded area between the unmod-ified and modified models thus indicates the modelinguncertainty introduced by the dust-cleaning step. Be-cause of this uncertainty and the lack of correction for,e.g., mode coupling, we do not report a formal goodnessof fit to the model; we simply note that at the 10% levelthe total power in the model appears to agree with thedata, particularly above (cid:96) = 1000.Somewhat more formally, we use the linear combina-tion framework to investigate the potential impact on8 L. Bleem, T. Crawford, et al.
500 1000 1500 2000 2500 300010 yy × datatSZCIBRadioTotal Figure 7.
Power spectrum of the CMB-CIB-nulled y map.The data points show the measured power spectrum of the y map from the three-component analysis in this work. Thepower spectrum is estimated using independent halves of thedata to avoid noise bias. Error bars are estimated using re-sampling of the values from the individual SPT-SZ fields.Lines show the expectation for power from various compo-nents in the y map, given the signal models used in the linearcombination algorithm. These are calculated by multiplyingthe model power spectra at each band by the band weightsfor the CMB-CIB-nulled y map and summing. The blue andgray shaded areas indicate the possible effect of dust clean-ing on the CIB (see text for details). The by-eye agreementbetween the solid black line (sum of all model components)and the data points indicates that the signal variance modelsare roughly representative of the true signals in the data. y -map variance from incorrect signal modeling. Thesignals in question have been reasonably well charac-terized in previous studies. The primary CMB temper-ature anisotropy has been measured at the percent levelin bins of ∆ (cid:96) ∼
50 (assuming a smooth power spectrum)by
Planck (Planck Collaboration et al. 2016j) and high-resolution ground-based experiments such as ACT (Choiet al. 2020) and SPT (Story et al. 2013). At (cid:96) = 3000,Reichardt et al. (2020) measures the relevant secondaryand foreground signals, namely the CIB and residual ra-dio galaxy power after masking, with ∼
10% precision.We create several sets of band weights using different sig-nal model inputs, modifying each input component byan amount that is in mild tension with current data. Foreach of these sets of band weights, we compute the pre-dicted variance in the output maps under the assump-tion that the modified inputs are correct and under theassumption that the original signal model was correct.Specifically, we modify the primary CMB power spec-trum by ±
2% in amplitude and ±
2% in spectral index,both of which are four to five times the marginalized error bar on the associated cosmological parameter orparameter combination ( A s e − τ and n s , respectively).We modify the amplitude of the input CIB model by ± . Detection of Clusters by the tSZ Effect
One natural test of the quality of a constructedCompton- y map is of its efficacy for the blind detectionof clusters via the tSZ effect. As noted in the Intro-duction, there have been several recent analyses under-taking cluster searches on combined Planck and ground-based data using ACT (Aghanim et al. 2019) and SPT-SZ data (Melin et al. 2020). These works have bothnoted significant improvement in cluster detection overdata from each sample alone with Melin et al. (2020)particularly quantifying such improvements as a func-tion of redshift. Here we will present the results of sucha cluster search on our minimum-variance Compton- y map, comparing our results to cluster samples reportedby the SPT-SZ (Bleem et al. 2015b) and Planck collab-orations (Planck Collaboration et al. 2016a).To conduct this search, we adopt an essentially iden-tical procedure to that used in previous searches forclusters in SPT data (see e.g., Bleem et al. 2015b for amore detailed description of the process). Our search isbased on the spatial-spectral filtering method presentedin Melin et al. (2006) and, as the y -map construction hasalready isolated the tSZ signal, we simply make use ofa spatial filter designed to optimally extract the clustersignal in the presence of noise. We adopt a projectedspherical β -model with β fixed to 1 (Cavaliere & Fusco-Femiano 1976) as the model of our cluster profile:∆ T = ∆ T (1 + θ /θ ) − (3 β − / (13)where the normalization ∆ T is a free parameter andthe core radius, θ c , is allowed to vary in twelve equallyspaced steps from 0 . (cid:48)
25 to 3 (cid:48) (as in previous SPT works)and additionally include θ c values of 5 (cid:48) , (cid:48) , (cid:48) , and 12 (cid:48) to allow for the detection of clusters of larger angu-lar extent (the latter now enabled by the inclusion ofthe Planck data). This filtering corresponds to scales of θ of approximately 1 . (cid:48) to 60 (cid:48) in the commonly usedArnaud et al. (2010) model of cluster pressure profiles.We run our cluster identification algorithm on theflat-sky version of each of the 19 SPT-SZ fields, adopt-ing a 1 . (cid:48)
25 beam as our transfer function. The noise9in these maps is composed of the astrophysical, instru-mental, and atmospheric noise that remains after themap combination process. We estimate this noise bysumming the power from each component of our sky +noise model (Section 3.2) by the appropriate 2D Fourierspace weights for each frequency map included in the y map. We also heavily penalize the noise at low k x , high k y where we are missing modes in the maps (Section3.4).The resulting SZ candidate list has 418 detections atsignal-to-noise ξ > ξ > . ξ > Planck data, the addition of radiopower in the noise covariance matrix used in the mapconstruction (this power was not included in the Bleemet al. 2015b noise model), as well as the additional mask-ing around bright sources (Section 2.3), we match ournew candidate list at ξ > ξ > .
5. Associating detections within 2 (cid:48) we recover473 matches with an average ratio in the detection sig-nificance ( ξ new /ξ SPT-SZ )=1.0 and standard deviation ofthis ratio of 0.2. We recover all confirmed SZ clusters(those with redshifts reported in Bleem et al. 2015b)above ξ = 6 . y footprintand 94% (85%) of confirmed clusters at ξ > ξ > . ξ > ξ = 1 .
4; there are no significantredshift or θ c trends in the unmatched clusters comparedto the matched.We note that a quick reading of this work may im-ply that the addition of Planck data did not contributein a meaningful way for the detection of these systems.However, we remind the reader that we have adopteda weighting scheme in the map construction that min-imizes the cross-correlation of the y map with the CIB(see Section 3.5) and adds a noise penalty to these mapscompared to a true minimum-variance y map. The ad-dition of the Planck data (and to a much lesser extentthe SPT-SZ 220 GHz data) essentially compensates forthis choice.Moving on to comparisons with the
Planck
SZ clustersample (Planck Collaboration et al. 2016h), we asso-ciate our new SZ candidate list with confirmed
Planck clusters within the larger of 4 (cid:48) or the
Planck positionaluncertainty, finding 103/117 matches at ξ >
Planck detection signal-to-noise ratio > . . × . This is an improvement over a similar match-ing exercise undertaken with the Bleem et al. (2015b)sample for which 83 SPT-SZ clusters in the Compton- y map footprint had matches to confirmed clusters inthe Planck catalog (see also discussion comparing prop-erties of the
Planck and SPT-SZ and SPT-ECS sam-ples in Bleem et al. 2020). The most significant gainswere found, as would be expected, for low- z clusterswith larger angular extent on the sky for which theinclusion of Planck data provides enhanced sensitivity.While the typical signal-to-noise of the combined mapSZ detections are higher than those from
Planck alone,our simplified treatment of the
Planck noise—both inthe map combination procedure as well as the clus-ter extraction (see e.g., discussion in Planck Collabo-ration et al. 2014d, 2016h for more optimal treatment of
Planck data)—leads to lower detection significances forthe lowest-redshift clusters.5.3. tSZ nulling in the CMB/kSZ maps
We perform one final validation test regarding the ef-ficiency of the tSZ nulling in the CMB/kSZ componentmaps. While the derivations governing both nulling andthe thermal SZ spectrum are unambiguous, this test willprobe both our constraints on the bandpasses and cali-bration of our maps as well as the presence of correlatedsignals not explicitly cancelled (from e.g., cluster mem-ber galaxies) at the locations of clusters; we note that asthese are SZ-selected clusters this is not a strong test ofthe presence of such associated emission in the generalcluster population (though see discussion of such effectsin e.g., Section 3.5 of Bleem et al. 2020). As our base-line we construct a true minimum-variance CMB/kSZmap and sum the temperature values in this map at thelocation of 504 confirmed SPT-SZ clusters with ξ > . − ± . µ K. Performingthis exercise on the CMB/kSZ maps with the tSZ- andtSZ/CIB-model nulled we find − ± µ K and 7 ± µ K,respectively.Sharpening our sensitivity to cluster scales, we thenrepeat this exercise, performing compensated aperturephotometry on the 3 maps with 2 (cid:48) apertures at the clus-ter locations. We again find a significant average tem-perature decrement in the minimum variance CMB map( − . ± . × − µ K-sr, 45 σ ), a small decrementin the tSZ-nulled maps ( − . ± . × − µ K-sr; 7.5 σ )and no significant detection in the tSZ/CIB-nulled maps(3 ± × − µ K-sr; 1.5 σ increment). As expected, the0 L. Bleem, T. Crawford, et al. minimum-variance CMB map shows a significant tem-perature decrement at the stacked location of these mas-sive systems in both tests and the results from tSZ/CIB-nulled maps are consistent with zero. At first glance,the significant decrement in the stack in the tSZ-nulledmap may indicate a problem in this map. However, wenote that owing to noise bias in the tSZ selection wewould not have expected complete cancellation in thetSZ-nulled CMB map. Recall the CIB is one of the dom-inant sources of astrophysical noise in the SPT maps atsmall scales (Reichardt et al. 2020) and indeed a stackof the SPT 220 GHz maps (whose effective frequency isat the tSZ null, Section 2.1.4) shows a small, but sig-nificant, average temperature decrement demonstratingthat the SPT-SZ cluster detection is slightly biased toareas with lower levels of CIB. Based on the weights inthe CMB/kSZ two component map (Figure 1) we wouldexpect a slight temperature decrement to remain at thelocation of SPT-selected clusters.The best way to robustly test these maps is with alarge cluster sample selected independently of any signalin the millimeter-wave maps. In lieu of such a sample,we perform a much more restricted test using opticallyselected clusters from the Blanco Cosmology Survey aspresented in Bleem et al. (2015a). Stacking a sample of169 lower-mass clusters at 0 . < z < . λ >
25 we find a 7 σ temperature decrement inthe minimum-variance CMB maps ( − . ± . × − µ K-sr) and no significant detection in the other two maps(0 ± × − µ K-sr and 2 ± × − µ K-sr in the tSZ- andtSZ/CIB-nulled maps respectively). Up to its limitedstatistical constraining power this test demonstrates theefficacy of tSZ removal in the tSZ-nulled map; we notethat much more constraining tests will soon become pos-sible with the release of eROSITA (Merloni et al. 2012)and Dark Energy Survey (Flaugher et al. 2015) Year 3cluster samples. SUMMARYIn this work we have presented new CMB/kSZ andCompton- y component maps from combined SPT-SZand Planck data. These maps, which cover 2442square-degrees of the Southern sky, represent a signif-icant improvement over previous such products avail-able in this region by virtue of their higher angularresolution (1 . (cid:48)
25 and 1 . (cid:48)
75 for the minimum-varianceand component-nulled products, respectively) and lowernoise at small angular scales. We have detailed the con-struction of these maps via the linear combination ofindividual frequency maps from the two experimentsincluding our technique for limiting the correlation ofour lowest-variance Compton- y map products with the CIB. The new component maps and associated dataproducts, as well as the individual frequency mapsfrom SPT-SZ used to construct these maps, are pub-licly available at http://pole.uchicago.edu/public/data/sptsz ymap and the NASA/LAMBDA website.We have performed several validation tests on thecomponent maps. Our analysis of the CMB-CIB-nulledCompton- y map power spectrum shows good agree-ment with expectations from our adopted sky model.A “blind” tSZ cluster search using matched-filter tech-niques demonstrated the expected performance relativeto such searches in SPT and Planck data alone. Finally,a validation test of our tSZ component nulling in theCMB/kSZ maps via stacking such maps at the locationof massive SZ-clusters, demonstrated effective removalof the tSZ signal.This paper represents the first release of Compton- y and CMB/kSZ component maps from the SPT col-laboration. We expect these maps—in combinationwith current surveys such as the Dark Energy Survey(Flaugher et al. 2015) and eROSITA (Predehl et al.2010; Merloni et al. 2012); and near-future galaxy sur-veys like LSST (LSST Science Collaboration et al. 2009),Euclid (Amendola et al. 2018), and SPHEREx (Dor´eet al. 2014)—to provide powerful constraints on bothcosmology and the evolution of the gas properties ofgalaxies, groups, and clusters across cosmic time. Asdetailed in this work, both high-resolution and high-frequency measurements are critical for improving thequality of such component maps. Such measurementswill be available in the coming years by the inclusionof low-noise 95, 150, and 220 GHz data from the ongo-ing SPT-3G (Benson et al. 2014) and Advanced ACTPol(Henderson et al. 2016) experiments, and even wider fre-quency coverage from future CMB experiments (SimonsObservatory Collaboration 2019; CMB-S4 Collaborationet al. 2019). ACKNOWLEDGEMENTSThe South Pole Telescope program is supported bythe National Science Foundation (NSF) through grantsPLR-1248097 and OPP-1852617. Partial support isalso provided by the NSF Physics Frontier Center grantPHY- 1125897 to the Kavli Institute of CosmologicalPhysics at the University of Chicago, the Kavli Foun-dation, and the Gordon and Betty Moore Foundationthrough grant GBMF Facilities:
NSF/US Department of Energy 10mSouth Pole Telescope (SPT-SZ),
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25 resolution. We provide maps in both HEALPix(N side =8192) and flat sky (0 . (cid:48)
25 pixelation) format.2. CMB-CIB-nulled Compton- y maps and Null noise maps at 1 . (cid:48)
75 resolution. HEALPix and flat sky format.3. Point sources masks and Dust masks.4. SPT-SZ frequency maps, PSDs, bandpasses, and transfer function plus beam estimates for the SPT-SZ mapsused to construct the component maps in this work. B. DERIVATION OF THE OPTIMAL LINEAR COMBINATIONIn this appendix, we provide an alternate derivation of the result that Equations 3, 4, and 5 represent, under theassumptions detailed in Section 3, the minimum-variance unbiased estimate of a map of signal S with SED f fromindividual frequency maps. As discussed in that section, we model the data in observing frequency ν i towards skydirection n as contributions from the signal of interest S and noise (including instrumental and astrophysical noiseand astrophysical signals other than S ). Neglecting beam and transfer function for now, we write: T ( ν i , n ) = f ( ν i ) S ( n ) + n ( ν i , n ) (B1)or, assuming pixelized data and using Roman indices for observing bands and Greek indices for map pixels: T iα = f i S α + n iα (B2)Adapting the derivation of Haehnelt & Tegmark (1996), we note that the most general linear estimator for S usingthe data from the individual maps is: ¯ S ( n ) = (cid:88) i (cid:90) W i ( n − n (cid:48) ) T ( ν i , n (cid:48) ) d x (cid:48) , (B3)or ¯ S α = (cid:88) i,β W iαβ T iβ . (B4)We require that ¯ S α be an unbiased estimate of S α : b α = (cid:104) ¯ S α − S α (cid:105) = 0 , (B5)and we wish to minimize the variance σ = (cid:42)(cid:88) α,β ( ¯ S α − S α )( ¯ S β − S β ) (cid:43) . (B6)If the noise in each map has zero mean ( (cid:104) n iα (cid:105) = 0), then b α = (cid:88) i,β W iαβ f i S β − S α , (B7)where σ = (cid:88) α,β b α b β + (cid:88) i,j,α,β,γ,δ W iαγ W jβδ (cid:104) n iγ n jδ (cid:105) (B8)6 L. Bleem, T. Crawford, et al.
Using the Lagrange multiplier λ α to enforce the constraint b = 0, we minimize the variance by taking the functionalderivative with respect to W iαβ of the quantity L = σ + (cid:88) α λ α b α (B9)and setting the result to zero. Even without solving for λ α , we see that, up to an overall constant, the contributionto the optimal estimator S α from the map at each individual frequency is simply the tSZ sensitivity weighted by theinverse band-band-pixel-pixel noise covariance matrix: W iαβ ∝ (cid:88) j (cid:104) n iα n jβ (cid:105) − f j , (B10)and the proportionality constant is easily obtained by enforcing equation B5, yielding: W iαβ = (cid:80) j (cid:104) n iα n jβ (cid:105) − f j (cid:80) i,j (cid:104) n iα n jβ (cid:105) − f i f j . (B11)If the various sources of noise in the individual maps can be modeled as Gaussian, random, statistically isotropicfields, then the spherical harmonic transform (or two-dimensional Fourier transform, in the flat-sky limit) of thepixel-pixel-band-band covariance matrix will be diagonal along the spatial frequency direction: SHT (cid:8) (cid:104) n iα n jβ (cid:105) − (cid:9) ≡ (cid:104) n i(cid:96) n j(cid:96) (cid:48) (cid:105) − (B12)= C − (cid:96)ij δ (cid:96)(cid:96) (cid:48) , where C (cid:96)ij is the spatial power spectrum of the noise in band ν i if j = i and the cross-spectrum of the noise in bands ν i and ν j if j (cid:54) = i . In this case we can rewrite equation B4 as:¯ S (cid:96) = (cid:88) i W i(cid:96) T i(cid:96) , (B13)where T i(cid:96) is the spherical harmonic transform (SHT) of the map in band ν i , ¯ S (cid:96) is the SHT of the estimated Compton- y map, and W i(cid:96) = (cid:80) j C − (cid:96)ij f j (cid:80) i,j C − (cid:96)ij f i f j . (B14)Equation 4 is the flat-sky, anisotropic version of Equation B14, including the beam and transfer function in f , suchthat f ( ν i ) → f ( ν i ) R ( ν i , l ). C. EQUIVALENCE TO OTHER FORMULATIONSEquation 3 in Madhavacheril et al. (2020), as derived in, e.g., Remazeilles et al. (2011a), gives the following expressionfor the optimal band weights for one signal component a ( ν ) while explicitly nulling another signal component a (cid:48) ( ν ): w i = (cid:16) a (cid:48) j C − jk a (cid:48) k (cid:17) a j C − ji − (cid:16) a j C − jk a (cid:48) k (cid:17) a (cid:48) j C − ji (cid:16) a j C − jk a k (cid:17) (cid:16) a (cid:48) j C − jk a (cid:48) k (cid:17) − (cid:16) a j C − jk a (cid:48) k (cid:17) . (C15)In this expression, summing over repeated indices is assumed, and the (cid:96) subscript has been omitted. Adopting thisconvention and, as in the previous appendix, neglecting beam and transfer function effects for simplicity, we can writewrite Equation 7 (our expression for multicomponent weights) as: ψ ij ≡ ψ i ( ν j ) = (cid:2) f T N − f (cid:3) − ik (cid:2) f T N − (cid:3) kj . (C16)(Incidentally, this is immediately recognizable as the solution to the least-squares problem, with f as the design matrixand N as the covariance matrix.) For the specific case of two components, we can rewrite f and ψ as f ij ≡ f i ( ν j ) = (cid:34) a ( ν j ) a (cid:48) ( ν j ) (cid:35) ≡ (cid:34) a j a (cid:48) j (cid:35) (C17)7 ψ ij ≡ ψ i ( ν j ) = (cid:34) w ( ν j ) w (cid:48) ( ν j ) (cid:35) ≡ (cid:34) w j w (cid:48) j (cid:35) . (C18)Also adopting C for the band-band covariance (as opposed to N ), we can write f T N − as (cid:2) f T N − (cid:3) ij ≡ (cid:2) f T C − (cid:3) ij = (cid:34) a k C − kj a (cid:48) k C − kj (cid:35) , (C19)and write f T N − f as (cid:2) f T N − f (cid:3) ij ≡ (cid:2) f T C − f (cid:3) ij = (cid:34) a k C − km a m a k C − km a (cid:48) m a (cid:48) k C − km a m a (cid:48) k C − km a (cid:48) m (cid:35) , (C20)Inverting this by hand (and noting that C is symmetric) yields (cid:2) f T C − f (cid:3) − ij = 1 (cid:0) a k C − km a m (cid:1) (cid:0) a (cid:48) k C − km a (cid:48) m (cid:1) − (cid:0) a k C − km a (cid:48) m (cid:1) (cid:34) a (cid:48) m C − km a (cid:48) m − a k C − km a (cid:48) m − a k C − km a (cid:48) m a k C − km a m (cid:35) , (C21)and applying the result to Equation C20 yields (cid:34) w j w (cid:48) j (cid:35) = 1 (cid:0) a k C − km a m (cid:1) (cid:0) a (cid:48) k C − km a (cid:48) m (cid:1) − (cid:0) a k C − km a (cid:48) m (cid:1) (cid:34) (cid:0) a (cid:48) k C − km a (cid:48) m (cid:1) a k C − kj − (cid:0) a k C − km a (cid:48) m (cid:1) a (cid:48) k C − kj (cid:0) a k C − km a m (cid:1) a (cid:48) k C − kj − (cid:0) a k C − km a (cid:48) m (cid:1) a k C − jk (cid:35) ,,